Irreversible Time, Reversible Mass: A Two-Layer Cyclic Cosmology from G-MaTT

Abstract We propose a singularity-free cyclic cosmology in which *only the mass torsional field* \(\hat{M}_\mu\) reverses, while *time itself remains irreversible*. In Generalized Mass as Twisted Time (G-MaTT), time emerges from cumulative phase branching in the primordial potential \(\mathcal{M}_\mu\), whereas mass and geometry arise from the torsional coherence of \(\hat{M}_\mu\)-braids. Desynchronization above thresholds \(v > c\sqrt{\alpha/w}\) or \(\omega > \Omega_0\sqrt{\alpha}/(2\pi w)\) produces dark matter and dark energy — but crucially, *re-locking is possible* when conditions reverse, restoring coherence without erasing phase history. We show that total entropy \(S = S_{\text{branch}} + S_{\text{sync}}\) increases monotonically (via irreversible branching), while the apparent low-entropy reset arises from oscillatory synchronization entropy. The universe thus recomposes — not repeats — across cycles. Predictions include: (i) CMB phase-gradient non-Gaussianity, (ii) a slowly decreasing cosmological constant across cycles, and (iii) torsion-echo gravitational wave bursts. This resolves the entropy problem of cyclic cosmologies without fine-tuning or new physics.